numpy和statsmodels在计算相关性时会给出不同的值，如何解释呢? [英] numpy and statsmodels give different values when calculating correlations, How to interpret this?

问题描述

我找不到使用numpy.correlate计算两个系列A和B之间的相关性与使用statsmodels.tsa.stattools.ccf

I can't find a reason why calculating the correlation between two series A and B using numpy.correlate gives me different results than the ones I obtain using statsmodels.tsa.stattools.ccf

以下是我提到的这种差异的一个示例:

Here's an example of this difference I mention:

import numpy as np
from matplotlib import pyplot as plt
from statsmodels.tsa.stattools import ccf

#Calculate correlation using numpy.correlate
def corr(x,y):
    result = numpy.correlate(x, y, mode='full')
    return result[result.size/2:]

#This are the data series I want to analyze
A = np.array([np.absolute(x) for x in np.arange(-1,1.1,0.1)])
B = np.array([x for x in np.arange(-1,1.1,0.1)])

#Using numpy i get this
plt.plot(corr(B,A))

#Using statsmodels i get this
plt.plot(ccf(B,A,unbiased=False))

结果似乎在质上有所不同，这种差异来自何处?

The results seem qualitatively different, where does this difference come from?

推荐答案

statsmodels.tsa.stattools.ccf是基于np.correlate的，但是还做了一些其他事情以统计意义而非信号处理意义给出相关性，请参见维基百科上的互相关.您可以在源代码中确切看到什么，这非常简单.

statsmodels.tsa.stattools.ccf is based on np.correlate but does some additional things to give the correlation in the statistical sense instead of the signal processing sense, see cross-correlation on Wikipedia. What happens exactly you can see in the source code, it's very simple.

为便于参考，我复制了以下相关行:

For easier reference I copied the relevant lines below:

def ccovf(x, y, unbiased=True, demean=True):
    n = len(x)
    if demean:
        xo = x - x.mean()
        yo = y - y.mean()
    else:
        xo = x
        yo = y
    if unbiased:
        xi = np.ones(n)
        d = np.correlate(xi, xi, 'full')
    else:
        d = n
    return (np.correlate(xo, yo, 'full') / d)[n - 1:]

def ccf(x, y, unbiased=True):
    cvf = ccovf(x, y, unbiased=unbiased, demean=True)
    return cvf / (np.std(x) * np.std(y))

这篇关于numpy和statsmodels在计算相关性时会给出不同的值，如何解释呢?的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！